The invention relates to a method for determining a rotor position angle of a synchronous machine. A synchronous machine generally consists of a stator provided with three-phase winding and a magnetised rotor. The rotor is typically magnetised either by means of permanent excitation or separate excitation. In permanent excitation the rotor is provided with permanent magnet blocks, which the magnetic field produced in the stator pulls towards itself, thereby rotating the rotor. Separate excitation of the rotor means that the rotor contains coils of wire to which current is supplied. The coils of wire thus form magnetic poles in the rotor, the poles functioning according to the same principle as poles made of permanent magnets. In addition, the rotor of the synchronous machine may be a salient-pole rotor or a cylindrical rotor. In cylindrical rotor machines the rotor inductance remains almost constant with respect to the stator, whereas in salient-pole machines, the rotor inductance varies greatly due to changes in the air gap between the rotor and the stator, depending on the rotor position angle.
In speed-controlled synchronous machines, it is important for the functioning of the control system that the position angle of the machine's rotor is known as precisely as possible. Particularly in control methods based on direct control of the machine's stator flux the accuracy of angle determination has a great influence on the accuracy of the control. The rotor position angle is usually determined using a pulse encoder or an absolute sensor the information supplied by which allows the rotor angle to be determined.
The measurement result obtained from the angle sensor contains errors caused at least by two different components that can be determined. The first known error-causing component is an incorrect initial angle, which is determined by an angle sensor. Various estimation algorithms have been proposed for estimating the initial angle. However, the rotor can be initially turned in a desired direction, provided that the motor load allows this. The rotor is preferably turned so that it is in the same direction as the coil of a phase, for example. The rotor can be turned by supplying direct current to the desired phase, thus causing the rotor to turn in the desired direction. However, due to the purposes of use of synchronous machines, it is often impossible to determine and correct the initial angle by turning the rotor.
In a salient-pole synchronous machine, such as a separately excited synchronous machine or one comprising permanent magnet magnetisation, or in a synchronous reluctance machine, the stator inductance Ls in stationary co-ordinates varies as a function of the rotor angle θr, as shown by the following equation:Ls=Ls0+Ls2 cos 2θr.
Inductance varies around the basic value Ls0 at twice the rotor angle in a magnitude indicated by the inductance coefficient Ls2. The inductance coefficients Ls0 and Ls2 are defined as follows:
            L      s0        =                            L          sd                +                  L          sq                    2        ,          ⁢            L      s2        =                            L          sd                -                  L          sq                    2        ,where the inductances Lsd ja Lsq represent the direct-axis and quadrature-axis transient inductances of the synchronous machine.
The utilization of the above equation for determining the initial angle of the rotor is known per se and discussed for example in S. Östlund and M. Brokemper, “Sensorless rotor-position detection from zero to rated speed for an integrated PM synchronous motor drive,” IEEE Transactions on Industry Applications, vol. 32, pp. 1158–1165, September/October 1996 and M. Schroedl, “Operation of the permanent magnet synchronous machine without a mechanical sensor,” in Int. Conf. on Power Electronics and Variable Speed Drives, pp. 51–55, 1990.
According to M. Leksell, L. Harnefors, and H.-P. Nee, “Machine design considerations for sensorless control of PM motors,” in Proceedings of the International Conference on Electrical Machines ICEM'98, pp. 619–624, 1998, sinusoidally altering voltage is supplied to a stator in the assumed direct-axis direction of the rotor. If this results in a quadrature-axis current in the assumed rotor coordinates, the assumed rotor coordinates are corrected such that the quadrature-axis current disappears. The reference states that a switching frequency of the frequency converter supplying the synchronous machine should be at least ten times the frequency of supply voltage. Thus, the maximum supply voltage frequency of a frequency converter capable of a 5 to 10 kHz switching frequency is between 500 and 1000 Hz. This is sufficient for an algorithm to function. Switching frequencies of this magnitude can be achieved by IGBT frequency converters, but with GTO or IGCT power-switch frequency converters, which are required at higher powers; the maximum switching frequency is less than 1 kHz. In that case the maximum frequency of the supply voltage in the initial angle estimation is below 100 Hz. At such a low frequency the machine develops torque and the accuracy of the algorithm is considerably impaired.
In the reference by M. Schroedl, 1990, the initial angle is calculated directly from one inductance measurement or, if more measurements are used, the additional information is utilized by eliminating inductance parameters. A drawback of this method is that an error, which is inevitable in measuring, has a great influence. To measure inductance, a current impulse is supplied to a stator and the flux linkage thereby caused is used to calculate the inductance. Errors may appear because of an error in the current measuring or because the measuring current produces torque, which swings the rotor.
In the method disclosed by S. Östlund, M. Brokemper, the rotor angle is not calculated directly, but the minimum inductance is searched for by starting the measurement of inductances in different directions, first at long intervals and then, as the minimum is being approached, by reducing the angular difference in successive measurements. Although it is not mentioned in the article, the method easily catches fictitious minima resulting from measuring errors and thus an error value may be extremely high.